Law of Sines - Derivation

Derivation

Make a triangle with the sides a, b, and c, and angles A, B, and C. Draw the altitude from vertex C to the side across c; by definition it divides the original triangle into two right angle triangles. Mark the length of this line h.

It can be observed that:

Therefore

and

Doing the same thing with the line drawn between vertex A and side a will yield:

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